Decision analysis: what does a decision tree depict to support choosing among alternatives under uncertainty?
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AOnly pictorial icons without logic
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BNodes and branches that represent decisions and chance events, plus their consequences
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CConsequences only, without the preceding choices
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DA list of equations rather than a graphic model
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ENone of the above
Answer
Correct Answer: Nodes and branches that represent decisions and chance events, plus their consequences
Explanation
Introduction / Context:A decision tree is a visual model to evaluate choices where outcomes are uncertain. It clarifies structure, probabilities, and payoffs, enabling expected-value or risk-sensitive comparisons.
Given Data / Assumptions:
- Alternatives exist with uncertain results.
- Probabilities and payoffs (costs/benefits) can be estimated.
- We seek what the diagram shows.
Concept / Approach:Decision nodes (squares) branch into alternatives. Chance nodes (circles) branch into outcomes with probabilities. Terminal nodes annotate consequences (payoffs). By rolling back the tree, analysts compute expected values and select a strategy.
Step-by-Step Solution:
Define decision alternatives and draw branches from a square node.From each alternative, add chance nodes for uncertainties with probabilities.Attach outcomes/payoffs to terminal nodes and evaluate via rollback.Verification / Alternative check:Comparing expected values or applying utility functions on the same tree yields consistent strategy choices.
Why Other Options Are Wrong:Icons without logic, consequences alone, or purely equations omit the structured branching that makes trees useful.
Common Pitfalls:Ignoring dependence between branches or misestimating probabilities; always document assumptions.
Final Answer:Nodes and branches that represent decisions and chance events, plus their consequences